Summary

In the full sample, we saw a marginal effect of shape: right handers’ vs. left handers’ LVF global bias is 15.89ms greater for square targets than for circles (95% CI [-5.99, 37.76], p = .08, one-sided). We also saw that the estimated LVF global bias difference was greater between strong right and left handers (EHI +/- 100: 23.51ms difference) than between the default handedness groups (EHI </> +-40: 11.67ms difference).

When we limit analysis to squares only and EHI extremes, strong left handers have a further reduced (very close to zero), but not reversed, LVF global bias.

Strong left handers’ estimated LVF global bias for squares (2.45ms, 95%CI [-15.18, 20.01]) is lower than for circles (7.20ms, 95%CI [-9.98, 24.37]), but this difference is not significant (-4.74ms, 95%CI [-29.10, 19.62], p = .35, one-sided). With squares and circles combined, strong left handers’ LVF global bias was 4.59ms (95%CI [-7.90, 16.98]).

The critical three-way interaction effect is stronger in this analysis of squares only and EHI extremes (34.68ms, 95%CI [11.35, 58.01], p = .002, one-sided). The three-way effect for the full sample with both shapes was 11.67ms (95%CI [0.65, 22.69], p = .019, one-sided), for the full sample with squares only it was 19.76ms (95%CI [4.11, 35.40], p = .006, one-sided), and for EHI extremes with both shapes it was 23.51ms (95% CI [7.10, 39.92], p = .0025, one-sided).

Analyses

Field by level by shape

Does the interaction of field by level differ depending on shape (square vs. circle), for extreme left and right handers (EHI +/- 100)?

Reaction time is modeled as a linear effect of field, level, and handedness, using data from every target-present trial with a “go” response:

lmer( rt ~ field*level*shape + (1 | subject) )

Extreme righties (EHI +100; n = 182)


Demographics
N Age (years) Education (years) Sex (M/F/O) EHI
182 29.87 (6.14) 14.34 (2.48) 96/85/1 100 (0)



Field by level by shape interaction (RT)
ANOVA: compare models with vs. without interaction term
npar AIC BIC logLik deviance Chisq Df p.value1
9 300,066.118 300,138.19 −150,024.059 300,048.118 - - -
10 300,065.772 300,145.851 −150,022.886 300,045.772 2.346 1 .126
1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html)


Field by level by shape interaction (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec shape_consec estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Square - Circle 16.819 10.981 Inf −4.704 38.341 1.532 .126
1 A positive number means LVF global bias is stronger for squares (as observed in pilot)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


Effect of field by level for each shape (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec shape estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Circle 20.314 7.675 Inf 5.272 35.357 2.647 .008
LVF - RVF Local - Global Square 37.133 7.854 Inf 21.74 52.526 4.728 <.0001
1 A positive number means global bias (faster RT for global)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


Global bias by field, by shape (RT)
contrast estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
RVF Local Circle - RVF Global Circle −6.596 5.44 Inf −17.257 4.065 −1.213 .225
LVF Local Circle - LVF Global Circle 13.718 5.415 Inf 3.105 24.332 2.533 .011
RVF Local Square - RVF Global Square 19.649 5.565 Inf 8.743 30.555 3.531 .0004
LVF Local Square - LVF Global Square 56.782 5.547 Inf 45.91 67.654 10.236 <.0001
1 A positive number means global bias (faster RT for global)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided, uncorrected


RT estimates by field, level, and shape
field level shape emmean SE df1 asymp.LCL2 asymp.UCL2
LVF Global Circle 670.484 12.95 Inf 645.103 695.865
LVF Local Circle 684.203 12.954 Inf 658.814 709.592
LVF Global Square 703.021 12.958 Inf 677.624 728.419
LVF Local Square 759.803 13.001 Inf 734.321 785.285
RVF Global Circle 685.713 12.958 Inf 660.317 711.11
RVF Local Circle 679.117 12.956 Inf 653.724 704.511
RVF Global Square 717.007 12.972 Inf 691.583 742.431
RVF Local Square 736.656 12.995 Inf 711.186 762.127
1 Z-approximation
2 Confidence level: 95%


Extreme lefties (EHI -100; n = 182)


Demographics
N Age (years) Education (years) Sex (M/F/O) EHI
138 30.07 (5.87) 14.68 (2.45) 81/56/1 -100 (0)



Field by level by shape interaction (RT)
ANOVA: compare models with vs. without interaction term
npar AIC BIC logLik deviance Chisq Df p.value1
9 225,667.688 225,737.218 −112,824.844 225,649.688 - - -
10 225,669.542 225,746.798 −112,824.771 225,649.542 0.146 1 .703
1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html)


Field by level by shape interaction (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec shape_consec estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Square - Circle −4.744 12.429 Inf −29.103 19.616 −0.382 .703
1 A positive number means LVF global bias is stronger for squares (as observed in pilot)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


Effect of field by level for each shape (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec shape estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Circle 7.197 8.672 Inf −9.799 24.193 0.83 .407
LVF - RVF Local - Global Square 2.454 8.904 Inf −14.997 19.905 0.276 .783
1 A positive number means global bias (faster RT for global)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


Global bias by field, by shape (RT)
contrast estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
RVF Local Circle - RVF Global Circle 3.914 6.137 Inf −8.114 15.942 0.638 .524
LVF Local Circle - LVF Global Circle 11.111 6.129 Inf −0.901 23.123 1.813 .07
RVF Local Square - RVF Global Square 37.616 6.312 Inf 25.244 49.988 5.959 <.0001
LVF Local Square - LVF Global Square 40.07 6.29 Inf 27.742 52.398 6.371 <.0001
1 A positive number means global bias (faster RT for global)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided, uncorrected


RT estimates by field, level, and shape
field level shape emmean SE df1 asymp.LCL2 asymp.UCL2
LVF Global Circle 623.203 15.518 Inf 592.788 653.618
LVF Local Circle 634.314 15.524 Inf 603.888 664.74
LVF Global Square 656.067 15.526 Inf 625.637 686.497
LVF Local Square 696.137 15.581 Inf 665.599 726.675
RVF Global Circle 649.546 15.523 Inf 619.122 679.97
RVF Local Circle 653.46 15.523 Inf 623.035 683.884
RVF Global Square 675.247 15.541 Inf 644.788 705.706
RVF Local Square 712.863 15.575 Inf 682.337 743.39
1 Z-approximation
2 Confidence level: 95%


Field by level by handedness by shape

Does the interaction of field by level by handedness differ depending on shape (square vs. circle), for extreme left and right handers (EHI +/- 100)?

Reaction time is modeled as a linear effect of field, level, handedness (EHI < -100 or EHI > +100), and shape, using data from every target-present trial with a “go” response:

lmer( rt ~ field * level * handedness * shape + (1 | subject) )

Demographics
Handedness N Age (years) Education (years) Sex (M/F/O) EHI
Left 138 30.07 (5.87) 14.68 (2.45) 81/56/1 -100 (0)
Right 182 29.87 (6.14) 14.34 (2.48) 96/85/1 100 (0)



4-way field by level by handedness by shape interaction (RT)
ANOVA: compare models with vs. without interaction term
npar AIC BIC logLik deviance Chisq Df p.value1
17 525,737.216 525,882.904 −262,851.608 525,703.216 - - -
18 525,737.534 525,891.791 −262,850.767 525,701.534 1.682 1 .195
1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html)


4-way field by level by handedness by shape interaction (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec handedness_consec shape_consec estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Right - Left Square - Circle 21.562 16.626 Inf −11.024 54.147 1.297 .195
1 A positive number means the interaction of field by level by handedness is stronger for squares
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


Effect of field by level by handedness for each shape (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec handedness_consec shape estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Right - Left Circle 13.118 11.609 Inf −9.635 35.87 1.13 .258
LVF - RVF Local - Global Right - Left Square 34.68 11.902 Inf 11.352 58.008 2.914 .004
1 A positive number means more LVF global bias for right handers
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


Effect of field by level by shape for each handedness group (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec shape_consec handedness estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Square - Circle Left −4.743 12.555 Inf −29.35 19.864 −0.378 .706
LVF - RVF Local - Global Square - Circle Right 16.818 10.899 Inf −4.544 38.18 1.543 .123
1 A positive number means more LVF global bias for right handers
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


Effect of field by level for each handedness group, by shape (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec handedness shape estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Left Circle 7.197 8.76 Inf −9.972 24.366 0.822 .411
LVF - RVF Local - Global Right Circle 20.315 7.618 Inf 5.385 35.245 2.667 .008
LVF - RVF Local - Global Left Square 2.454 8.994 Inf −15.175 20.082 0.273 .785
LVF - RVF Local - Global Right Square 37.133 7.795 Inf 21.855 52.412 4.764 <.0001
1 A positive number means LVF global bias
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


Plots

Error bars show 95% CI. Left handers are those with EHI = -100; Right handers, EHI = +100.